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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Kirkwood approximation ： ウィキペディア英語版 Kirkwood approximation The Kirkwood superposition approximation was introduced in 1935 by John G. Kirkwood as a means of representing a discrete probability distribution.〔Kirkwood, J. G. ''Statistical Mechanics of Fluid Mixtures''. J. Chem. Phys. 3, 300, (1935)〕 The Kirkwood approximation for a discrete probability density function $P(x\_,x\_,\backslash ldots\; ,x\_)$ is given by :$$ P^(x_1,x_2,\ldots ,x_n)=\frac\subseteq \mathcal}p(\mathcal_)}\subseteq \mathcal}p(\mathcal_)}}}}p(\mathcal_1)} where : $\backslash prod\_\}p(\backslash mathcal\_i)$ is the product of probabilities over all subsets of variables of size ''i'' in variable set $\backslash scriptstyle\backslash mathcal$. This kind of formula has been considered by Watanabe (1960) and, according to Watanabe, also by Robert Fano. For the three-variable case, it reduces to simply :$$ P^\prime(x_1,x_2,x_3)=\frac The Kirkwood approximation does not generally produce a valid probability distribution (the normalization condition is violated). Watanabe claims that for this reason informational expressions of this type are not meaningful, and indeed there has been very little written about the properties of this measure. The Kirkwood approximation is the probabilistic counterpart of the interaction information. Judea Pearl (1988 §3.2.4) indicates that an expression of this type can be exact in the case of a ''decomposable'' model, that is, a probability distribution that admits a graph structure whose cliques form a tree. In such cases, the numerator contains the product of the intra-clique joint distributions and the denominator contains the product of the clique intersection distributions. == References == * Jakulin, A. & Bratko, I. (2004), Quantifying and visualizing attribute interactions: An approach based on entropy, ''Journal of Machine Learning Research'', (submitted) pp. 38–43. * Matsuda, H. (2000), Physical nature of higher-order mutual information: Intrinsic correlations and frustration, ''Physical Review E'' 62, 3096–3102. * Pearl, J. (1988), ''Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference'', Morgan Kaufmann, San Mateo, CA. * Watanabe, S. (1960), Information theoretical analysis of multivariate correlation, ''IBM Journal of Research and Development'' 4, 66–82. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Kirkwood approximation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.